The present invention generally relates to a process control method. More particularly, the invention is directed to a process control system for controlling a process exhibiting both linear and non-linear behaviors by a combination of control quantities of control effectors including a plurality of digital or analogue quantities.
In recent years, approaches for application of the fuzzy theory to actual processes on a real time basis have been vigorously studied in the field of control techniques and some practical applications are reported. The basic concept of this fuzzy theory is based on the stand point that "a theoretical system established definitely can not exceed a certain boundary or circumscription", and thus the behavior of an actual process subject to a control of concern which includes inevitably non-linear elements can not be controlled in a perfectly satisfactory manner only with the control method which relies on mathematical expressions representing physical models. Introduction and application of the fuzzy theory to control systems may be explained by the fact that because of very large scale and complex implementation of modern control systems, an extreme difficulty is encountered in making available the accurate information required for the processing executed by the computer at the present state of the art. As the scale of the control system becomes larger, the number of the non-linear elements increases correspondingly, making it impractical or impossible to describe the process accurately with mathematical expressions. Under the circumstances, fuzziness accompanying the action taken by an operator partaking in a process control system is assuming an important role in the process control.
In the following, some examples of the control systems relying upon the conventional control procedure based on mathematical models and applied fuzzy theory will be discussed to make clear the problems to be coped with by the present invention.
As typical example of a conventional control system based on mathematical models and including a large number of non-linear elements and lots of fuzziness, let's consider a longitudinal flow type ventilation control system adopted in the management of a huge tunnel having a great length.
Construction of rapid transit roadways fluorishing in these years are attended with constructions and use of the long tunnel in an increasing number. Also in the future, it is expected that the number of the long tunnels will increase for many reasons such as need for exploitation of the shortest route to a destination, difficulty in acquisition of the site for the construction and progress in the civil engineering technology.
In connection with operation and use of the tunnel for the transit roadway, ventilation equipment is indispensably required in order to protect the car drivers from the danger of exhaust gases and ensure the safety of persons engaging in maintenance. In conjunction with the ventilation for the long tunnel, it is noted that although the transverse type ventilation system employing ventilation ducts installed in the extending direction of the tunnel have been employed in many cases in view of high performance of the ventilation, the longitudinal type ventilation system including a combination of jet fans (blowers) and dust/dirt collectors is taking on the leading role in recent years because of low costs for installation and facility of the maintenance.
In either one of the ventilation systems mentioned above, the most important problem is how to satisfy the requirements imposed on the running cost of the ventilation equipment on one hand and the quality of ventilation on the other hand, which requirements or conditions however are in a reciprocal relation. Heretofore, problems of non-linearity (uncertainty) involved in the prediction of a turbulent diffusion phenomenon and a pollution genesis mechanism inherent to the tunnel ventilation process have been dealt with only by linear control relying on mathematical models. Accordingly, the satisfactory result of the control can be obtained only when the ventilation process exhibits linearity. If otherwise, the control process can not afford a satisfactory result.
FIG. 2 of the accompanying drawings is a conceptual view illustrating control factors in a longitudinal type long tunnel ventilation control system. Jet fans or blowers 7 and dust collectors 8 constituting parts of the ventilation equipment controlled by a control apparatus 1 are indispensable members playing an important role in retaining the concentration of pollution gases such as CO, NO.sub.s, SO.sub.x and others noxious to the human body and smog harmful to the safety of the drive. Since the electric power consumed by these jet fans and the dust collectors occupies a large proportion of the electric power consumption of the whole equipment, there exists an insistent demand for the efficient operation of these facilities. In other words, the tunnel ventilation control has to satisfy simultaneously two contradicting requirements, i.e. safety and economy, as mentioned above. As a control system adopted in the practical application for coping with the above requirements, there can be mentioned a so-called traffic flow prediction feed-forward control system.
FIG. 3 of the accompanying drawing is a view for illustrating the principle underlying the traffic prediction feed-forward control system mentioned above. For expressing or grasping the tunnel ventilation process in the form of a mathematical model, the tunnel is divided into n sections by taking into consideration the conditions such as slope, positions where the ventilation machines are installed and others. On the condition, the state within each section for ventilation can be expressed by a difference equation mentioned below. ##EQU1## where X(k+1) represents an average concentration of pollution within a ventilation section of concern at a time point K(t=kT), P(k) represents an amount of pollution generated within the ventilation section of concern during a period k(kT.ltoreq.t.ltoreq.(k+1)T), and Q(k) represents ventilation airflow within the ventilation section of concern during a period k(kT.ltoreq.t.ltoreq.(k+1)T).
When a standard or reference pollution quantity generated within the tunnel of concern is represented by P* with Q* representing a reference ventilation flow quantity for maintaining a reference pollution concentration X* corresponding to the quantity P*, there can validly be derived from the expression (1) the following expression: EQU Q*=P*/X* (2)
For determining a corrected ventilation when the concentration of pollution X(k) and the generated pollution quantity P(k) at the current time point k deviate from the respective reference quantities, variations between the actual quantities and the associated reference quantities are defined as follows: ##EQU2##
By substitution of the expressions (3) in the expression (1) and through linear approximation in the neighborhood of the reference quantity, there can be obtained the following system equation; ##EQU3## In the above equation, considering .DELTA.X(k) as representing a state variable, .DELTA.Q(k) as representing a control variable and .DELTA.P(k) as representing an input variable, there can be realized a quantitative expression for the system. However, what it expressed by this equation is only a few parts of the process behaviors, as will hereinafter be made clear. For configuring the control system, it is required at the next stage to introduce an objective function. At this juncture, it is presumed that the object of the ventilation control mentioned above is to decrease the electric power consumption to a minimum while maintaining the concentration of pollution at the reference or standard level as far as possible. This presumption can be expressed in the form of a function as follows: ##EQU4##
In the above expression, the first term of the left-hand side concerns the safety and the second term concerns the economy, wherein F.sub.X and F.sub.Q are the coefficients for adjusting the weight assigned to these terms, respectively. In accordance with a known linear regulator theory, the corrected ventilation airflow .DELTA.Q.degree.(k) which minimizes the objective function given by the expression (5) can be determined from the system equation as follows:
where G.sub.X (k) and G.sub.P (k) represent feedback gains for .DELTA.X(k) and .DELTA.P(k), respectively.
A control system realized through repetition of the linear approximation procedures described above is shown in FIG. 4. Assuming in this control system that the concentration quantity (the level of the concentration) X(k) at a time point k can be determined accurately on the basis of a pollution sensor, it is believed that the improvement of the control accuracy will then depend only on the improvement of accuracy with which the traffic at a time point (k+1) can be predicted, because ##EQU5## where c.sub.j represents the amount of pollution generated by one motor vehicle of type j, and n.sub.j (k) represents the traffic amount (the number of motor vehicles) during the period k(kT.ltoreq.t.ltoreq.(k+1)T) on the assumption that the amount of pollution as generated is in proportion to the number of motor vehicles or cars transited during the period k. In this conjunction, prediction of the car transit number (i.e. the number of the cars transited during the period k) can be carried out, for example, by installing traffic counter sensors (hereinafter also referred to as the TC in abridgement) at the entrance and the exit of a tunnel, respectively, and by taking advantage of the fact that a linear relation exists in covariance among the time-series traffic data for the tunnel section of concern. Now, examples of the actually performed control based on the traffic prediction feed-forward control principle will be described by reference to FIGS. 5 to 7 of the accompanying drawings.
FIG. 5 shows transitions in the traffic and pollution quantities, respectively, during an elongated control period, i.e. when the ventilation airflow is made approximately constant. As will be seen from the graphs, there exists high correlation between the traffic quantity and the amount of pollution as produced. Further, the graphs show that the environment standard value (80 ppm in the case of the illustrated example) has been exceeded several times, indicating a low quality or performance of the ventilation (degraded safety). On the other hand, in the case of the control illustrated in FIG. 6 where the traffic prediction feedforward control has been performed for a period of ten minutes, the concentration value of CO converges to the objective value. Further, it can be seen that the electric power consumption is also improved when compared with the example shown in FIG. 5.
FIG. 7 illustrates, by way of example, the situation existing in the middle of the night where the traffic rate is low during a period of the same duration. Although it is obvious from the graphs that the ventilator operation is not required because the traffic is low absolutely, the ventilator is thrown into operation several times, consuming a large amount of electric power. The actual operation of the system adopting the traffic prediction feed-forward control will be what is mentioned below. On the basis of empirical knowledge, the operator usually takes the following procedures:
(1) In the middle of the night, the operator changes over the automatic operation control to the manual operation control on the basis of judgment of the total traffic quantity and the rate of change thereof. This manual operation control is continued to the rush-hour time in the morning.
(2) In case the change in the traffic flow is remarkable even in the daytime such as on a holiday, the control is changed over to the manual operation control.
(3) On a rainy day, the manual operation control is performed at a lower value than the controlled ventilation quantity outputted from the automatic control operation system, and so forth.
As will be seen, specific operations are performed through intervention by the operator in accordance with various rules established empirically by the operator. Considering the traffic control in terms of a general process control, there exist such situations in which the process behaves linearly, utterly non-linearly and partially linearly, respectively. This can be explained by the fact that the non-linear components in the various controls have heretofore been attempted to be handled by a linear equation as the external disturbance elements. Accordingly, when the external disturbance becomes a leading factor in the process behavior, there arises the necessity for another system description. In general, the control system such as the tunnel ventilation control includes many elements or components which are fuzzy for the description of the control. Besides, these elements compete with one another for the control of the process behavior from time to time. For these reasons, the quantitative expressions of these disturbance elements are very difficult.
FIG. 8 shows in a network diagram the main causes or factors for the pollution produced within a tunnel as confirmed by resorting to all the conceivable means such as simulation, actual measurements and others. As can be seen in the figure, the number of the causes or factors affecting the environment by producing pollution amounts are more than twelve, inclusive of the medium factors. All of these factors are of such a nature that they behave linearly at one time and non-linearly at another time. Besides, these factors may bear relation to one another at one time while no relation can be found at another time.
FIG. 9 shows in a network diagram similar to FIG. 8 the factors or causes participating in the ventilation. As can be seen in the figure, a weather phenomenon such as natural airflow plays an important role as well.
As will now be appreciated from the foregoing description, the serious problem of the hitherto known ventilation control system based on a mathematical model can be seen in that the ventilation control system can no longer be used tolerably except for the period during which all the factors behave linearly, as is discussed in detail in an article entitled "A New Ventilation Control For Long Road Tunnel" contained in a collection of articles and reports published in the Japan Society of Civil Engineers, No. 265 (1977).
In contrast to the control based on a mathematical model as described above, the fuzzy control is characterized in that the behaviors of factors affecting a process are expressed in terms of fuzzy quantities, wherein the final control quantities to be outputted are derived by transforming the fuzzy values having proper acceptance into quantitative values. However, the fuzzy control known heretofore suffers from shortcomings mentioned below.
First, a large number of items exist for the fuzzy evaluation, wherein evaluation for deriving a conclusion (operation control quantity) from the items is not only impractical but also difficult to understand.
Another disadvantage lies in that the fuzzy control may become more ineffective than the control based on a linear control model, depending on the situations, because the control based on the fuzzy quantities are applied even to such process phase which can be controlled with a high accuracy by the conventional linear model based control. This can be explained by the tendency that a process subject to the control is grasped definitely either as a process oriented for fuzzy control or as a process suited for linear control. The prior art fuzzy control is disclosed in detail, for example, in JP-A-58-19207 and JP-A-59-204707.
It is safe to say that processes in the real world are, more or less, extremely complicated combinations of linear behaviors and non-linear behaviors and thus it is impossible to realize an optimum control for all the situations with one definite control procedure.